{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tutorial \n",
    "\n",
    "Let us consider chapter 7 of the excellent treatise on the subject of Exponential Smoothing By Hyndman and Athanasopoulos [1].\n",
    "We will work through all the examples in the chapter as they unfold.\n",
    "\n",
    "[1] [Hyndman, Rob J., and George Athanasopoulos. Forecasting: principles and practice. OTexts, 2014.](https://www.otexts.org/fpp/7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exponential smoothing\n",
    "\n",
    "First we load some data. We have included the R data in the notebook for expedience."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-12-07T12:39:15.020317Z",
     "start_time": "2017-12-07T12:39:14.263100Z"
    }
   },
   "outputs": [],
   "source": [
    "import os\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from statsmodels.tsa.api import ExponentialSmoothing, SimpleExpSmoothing, Holt\n",
    "\n",
    "data = [446.6565,  454.4733,  455.663 ,  423.6322,  456.2713,  440.5881, 425.3325,  485.1494,  506.0482,  526.792 ,  514.2689,  494.211 ]\n",
    "index= pd.date_range(start='1996', end='2008', freq='A')\n",
    "oildata = pd.Series(data, index)\n",
    "\n",
    "data = [17.5534,  21.86  ,  23.8866,  26.9293,  26.8885,  28.8314, 30.0751,  30.9535,  30.1857,  31.5797,  32.5776,  33.4774, 39.0216,  41.3864,  41.5966]\n",
    "index= pd.date_range(start='1990', end='2005', freq='A')\n",
    "air = pd.Series(data, index)\n",
    "\n",
    "data = [263.9177,  268.3072,  260.6626,  266.6394,  277.5158,  283.834 , 290.309 ,  292.4742,  300.8307,  309.2867,  318.3311,  329.3724, 338.884 ,  339.2441,  328.6006,  314.2554,  314.4597,  321.4138, 329.7893,  346.3852,  352.2979,  348.3705,  417.5629,  417.1236, 417.7495,  412.2339,  411.9468,  394.6971,  401.4993,  408.2705, 414.2428]\n",
    "index= pd.date_range(start='1970', end='2001', freq='A')\n",
    "livestock2 = pd.Series(data, index)\n",
    "\n",
    "data = [407.9979 ,  403.4608,  413.8249,  428.105 ,  445.3387,  452.9942, 455.7402]\n",
    "index= pd.date_range(start='2001', end='2008', freq='A')\n",
    "livestock3 = pd.Series(data, index)\n",
    "\n",
    "data = [41.7275,  24.0418,  32.3281,  37.3287,  46.2132,  29.3463, 36.4829,  42.9777,  48.9015,  31.1802,  37.7179,  40.4202, 51.2069,  31.8872,  40.9783,  43.7725,  55.5586,  33.8509, 42.0764,  45.6423,  59.7668,  35.1919,  44.3197,  47.9137]\n",
    "index= pd.date_range(start='2005', end='2010-Q4', freq='QS-OCT')\n",
    "aust = pd.Series(data, index)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simple Exponential Smoothing\n",
    "Lets use Simple Exponential Smoothing to forecast the below oil data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-12-07T12:39:15.189907Z",
     "start_time": "2017-12-07T12:39:15.022229Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Figure 7.1: Oil production in Saudi Arabia from 1996 to 2007.\n"
     ]
    }
   ],
   "source": [
    "ax=oildata.plot()\n",
    "ax.set_xlabel(\"Year\")\n",
    "ax.set_ylabel(\"Oil (millions of tonnes)\")\n",
    "plt.show()\n",
    "print(\"Figure 7.1: Oil production in Saudi Arabia from 1996 to 2007.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we run three variants of simple exponential smoothing:\n",
    "1. In ```fit1``` we do not use the auto optimization but instead choose to explicitly provide the model with the $\\alpha=0.2$ parameter\n",
    "2. In ```fit2``` as above we choose an $\\alpha=0.6$\n",
    "3. In ```fit3``` we allow statsmodels to automatically find an optimized $\\alpha$ value for us. This is the recommended approach."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-12-07T12:39:15.785068Z",
     "start_time": "2017-12-07T12:39:15.191930Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fit1 = SimpleExpSmoothing(oildata).fit(smoothing_level=0.2,optimized=False)\n",
    "fcast1 = fit1.forecast(3).rename(r'$\\alpha=0.2$')\n",
    "fit2 = SimpleExpSmoothing(oildata).fit(smoothing_level=0.6,optimized=False)\n",
    "fcast2 = fit2.forecast(3).rename(r'$\\alpha=0.6$')\n",
    "fit3 = SimpleExpSmoothing(oildata).fit()\n",
    "fcast3 = fit3.forecast(3).rename(r'$\\alpha=%s$'%fit3.model.params['smoothing_level'])\n",
    "\n",
    "ax = oildata.plot(marker='o', color='black', figsize=(12,8))\n",
    "fcast1.plot(marker='o', ax=ax, color='blue', legend=True)\n",
    "fit1.fittedvalues.plot(marker='o', ax=ax, color='blue')\n",
    "fcast2.plot(marker='o', ax=ax, color='red', legend=True)\n",
    "\n",
    "fit2.fittedvalues.plot(marker='o', ax=ax, color='red')\n",
    "fcast3.plot(marker='o', ax=ax, color='green', legend=True)\n",
    "fit3.fittedvalues.plot(marker='o', ax=ax, color='green')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Holt's Method\n",
    "\n",
    "Lets take a look at another example.\n",
    "This time we use air pollution data and the Holt's Method.\n",
    "We will fit three examples again.\n",
    "1. In ```fit1``` we again choose not to use the optimizer and provide explicit values for $\\alpha=0.8$ and $\\beta=0.2$\n",
    "2. In ```fit2``` we do the same as in ```fit1``` but choose to use an exponential model rather than a Holt's additive model.\n",
    "3. In ```fit3``` we used a damped versions of the Holt's additive model but allow the dampening parameter $\\phi$ to be optimized while fixing the values for $\\alpha=0.8$ and $\\beta=0.2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-12-07T12:39:16.114361Z",
     "start_time": "2017-12-07T12:39:15.786542Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fit1 = Holt(air).fit(smoothing_level=0.8, smoothing_slope=0.2, optimized=False)\n",
    "fcast1 = fit1.forecast(5).rename(\"Holt's linear trend\")\n",
    "fit2 = Holt(air, exponential=True).fit(smoothing_level=0.8, smoothing_slope=0.2, optimized=False)\n",
    "fcast2 = fit2.forecast(5).rename(\"Exponential trend\")\n",
    "fit3 = Holt(air, damped=True).fit(smoothing_level=0.8, smoothing_slope=0.2)\n",
    "fcast3 = fit3.forecast(5).rename(\"Additive damped trend\")\n",
    "\n",
    "ax = air.plot(color=\"black\", marker=\"o\", figsize=(12,8))\n",
    "fit1.fittedvalues.plot(ax=ax, color='blue')\n",
    "fcast1.plot(ax=ax, color='blue', marker=\"o\", legend=True)\n",
    "fit2.fittedvalues.plot(ax=ax, color='red')\n",
    "fcast2.plot(ax=ax, color='red', marker=\"o\", legend=True)\n",
    "fit3.fittedvalues.plot(ax=ax, color='green')\n",
    "fcast3.plot(ax=ax, color='green', marker=\"o\", legend=True)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Seasonally adjusted data\n",
    "Lets look at some seasonally adjusted livestock data. We fit five Holt's models.\n",
    "The below table allows us to compare results when we use exponential versus additive and damped versus non-damped.\n",
    " \n",
    "Note: ```fit4``` does not allow the parameter $\\phi$ to be optimized by providing a fixed value of $\\phi=0.98$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-12-07T12:39:16.605618Z",
     "start_time": "2017-12-07T12:39:16.116424Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SES</th>\n",
       "      <th>Holt's</th>\n",
       "      <th>Exponential</th>\n",
       "      <th>Additive</th>\n",
       "      <th>Multiplicative</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>$\\alpha$</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.974306</td>\n",
       "      <td>0.977633</td>\n",
       "      <td>0.978847</td>\n",
       "      <td>0.974911</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\beta$</th>\n",
       "      <td>NaN</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\phi$</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.980000</td>\n",
       "      <td>0.981646</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$l_0$</th>\n",
       "      <td>263.917700</td>\n",
       "      <td>258.882647</td>\n",
       "      <td>260.341560</td>\n",
       "      <td>257.357648</td>\n",
       "      <td>258.951730</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$b_0$</th>\n",
       "      <td>NaN</td>\n",
       "      <td>5.010775</td>\n",
       "      <td>1.013780</td>\n",
       "      <td>6.644538</td>\n",
       "      <td>1.038145</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SSE</th>\n",
       "      <td>6761.350218</td>\n",
       "      <td>6004.138200</td>\n",
       "      <td>6104.194746</td>\n",
       "      <td>6036.555004</td>\n",
       "      <td>6081.995045</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  SES       Holt's  Exponential     Additive  Multiplicative\n",
       "$\\alpha$     1.000000     0.974306     0.977633     0.978847        0.974911\n",
       "$\\beta$           NaN     0.000000     0.000000     0.000000        0.000000\n",
       "$\\phi$            NaN          NaN          NaN     0.980000        0.981646\n",
       "$l_0$      263.917700   258.882647   260.341560   257.357648      258.951730\n",
       "$b_0$             NaN     5.010775     1.013780     6.644538        1.038145\n",
       "SSE       6761.350218  6004.138200  6104.194746  6036.555004     6081.995045"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fit1 = SimpleExpSmoothing(livestock2).fit()\n",
    "fit2 = Holt(livestock2).fit()\n",
    "fit3 = Holt(livestock2,exponential=True).fit()\n",
    "fit4 = Holt(livestock2,damped=True).fit(damping_slope=0.98)\n",
    "fit5 = Holt(livestock2,exponential=True,damped=True).fit()\n",
    "params = ['smoothing_level', 'smoothing_slope', 'damping_slope', 'initial_level', 'initial_slope']\n",
    "results=pd.DataFrame(index=[r\"$\\alpha$\",r\"$\\beta$\",r\"$\\phi$\",r\"$l_0$\",\"$b_0$\",\"SSE\"] ,columns=['SES', \"Holt's\",\"Exponential\", \"Additive\", \"Multiplicative\"])\n",
    "results[\"SES\"] =            [fit1.params[p] for p in params] + [fit1.sse]\n",
    "results[\"Holt's\"] =         [fit2.params[p] for p in params] + [fit2.sse]\n",
    "results[\"Exponential\"] =    [fit3.params[p] for p in params] + [fit3.sse]\n",
    "results[\"Additive\"] =       [fit4.params[p] for p in params] + [fit4.sse]\n",
    "results[\"Multiplicative\"] = [fit5.params[p] for p in params] + [fit5.sse]\n",
    "results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plots of Seasonally Adjusted Data\n",
    "The following plots allow us to evaluate the level and slope/trend components of the above table's fits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-12-07T12:39:17.105928Z",
     "start_time": "2017-12-07T12:39:16.607306Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Figure 7.4: Level and slope components for Holt’s linear trend method and the additive damped trend method.\n"
     ]
    }
   ],
   "source": [
    "for fit in [fit2,fit4]:\n",
    "    pd.DataFrame(np.c_[fit.level,fit.slope]).rename(\n",
    "        columns={0:'level',1:'slope'}).plot(subplots=True)\n",
    "plt.show()\n",
    "print('Figure 7.4: Level and slope components for Holt’s linear trend method and the additive damped trend method.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparison\n",
    "Here we plot a comparison Simple Exponential Smoothing and Holt's Methods for various additive, exponential and damped combinations. All of the models parameters will be optimized by statsmodels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-12-07T12:39:18.038995Z",
     "start_time": "2017-12-07T12:39:17.108323Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Figure 7.5: Forecasting livestock, sheep in Asia: comparing forecasting performance of non-seasonal methods.\n"
     ]
    }
   ],
   "source": [
    "fit1 = SimpleExpSmoothing(livestock2).fit()\n",
    "fcast1 = fit1.forecast(9).rename(\"SES\")\n",
    "fit2 = Holt(livestock2).fit()\n",
    "fcast2 = fit2.forecast(9).rename(\"Holt's\")\n",
    "fit3 = Holt(livestock2, exponential=True).fit()\n",
    "fcast3 = fit3.forecast(9).rename(\"Exponential\")\n",
    "fit4 = Holt(livestock2, damped=True).fit(damping_slope=0.98)\n",
    "fcast4 = fit4.forecast(9).rename(\"Additive Damped\")\n",
    "fit5 = Holt(livestock2, exponential=True, damped=True).fit()\n",
    "fcast5 = fit5.forecast(9).rename(\"Multiplicative Damped\")\n",
    "\n",
    "ax = livestock2.plot(color=\"black\", marker=\"o\", figsize=(12,8))\n",
    "livestock3.plot(ax=ax, color=\"black\", marker=\"o\", legend=False)\n",
    "fcast1.plot(ax=ax, color='red', legend=True)\n",
    "fcast2.plot(ax=ax, color='green', legend=True)\n",
    "fcast3.plot(ax=ax, color='blue', legend=True)\n",
    "fcast4.plot(ax=ax, color='cyan', legend=True)\n",
    "fcast5.plot(ax=ax, color='magenta', legend=True)\n",
    "ax.set_ylabel('Livestock, sheep in Asia (millions)')\n",
    "plt.show()\n",
    "print('Figure 7.5: Forecasting livestock, sheep in Asia: comparing forecasting performance of non-seasonal methods.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-10-05T09:40:15.958575Z",
     "start_time": "2017-10-05T09:40:15.615Z"
    }
   },
   "source": [
    "## Holt's Winters Seasonal\n",
    "Finally we are able to run full Holt's Winters Seasonal Exponential Smoothing  including a trend component and a seasonal component.\n",
    "statsmodels allows for all the combinations including as shown in the examples below:\n",
    "1. ```fit1``` additive trend, additive seasonal of period ```season_length=4``` and the use of a Box-Cox transformation.\n",
    "1. ```fit2``` additive trend, multiplicative seasonal of period ```season_length=4``` and the use of a Box-Cox transformation..\n",
    "1. ```fit3``` additive damped trend, additive seasonal of period ```season_length=4``` and the use of a Box-Cox transformation.\n",
    "1. ```fit4``` additive damped trend, multiplicative seasonal of period ```season_length=4``` and the use of a Box-Cox transformation.\n",
    "\n",
    "The plot shows the results and forecast for ```fit1``` and ```fit2```.\n",
    "The table allows us to compare the results and parameterizations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-12-07T12:39:28.375871Z",
     "start_time": "2017-12-07T12:39:18.040674Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\holtwinters.py:712: ConvergenceWarning: Optimization failed to converge. Check mle_retvals.\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\holtwinters.py:712: ConvergenceWarning: Optimization failed to converge. Check mle_retvals.\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Figure 7.6: Forecasting international visitor nights in Australia using Holt-Winters method with both additive and multiplicative seasonality.\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Additive</th>\n",
       "      <th>Multiplicative</th>\n",
       "      <th>Additive Dam</th>\n",
       "      <th>Multiplica Dam</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>$\\alpha$</th>\n",
       "      <td>4.546195e-01</td>\n",
       "      <td>3.659543e-01</td>\n",
       "      <td>6.194917e-09</td>\n",
       "      <td>0.000190</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\beta$</th>\n",
       "      <td>3.682627e-25</td>\n",
       "      <td>2.230501e-20</td>\n",
       "      <td>2.244538e-10</td>\n",
       "      <td>0.000190</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\phi$</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>9.429509e-01</td>\n",
       "      <td>0.912804</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\gamma$</th>\n",
       "      <td>5.244412e-01</td>\n",
       "      <td>3.232564e-14</td>\n",
       "      <td>2.917832e-07</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$l_0$</th>\n",
       "      <td>1.421751e+01</td>\n",
       "      <td>1.454813e+01</td>\n",
       "      <td>1.415722e+01</td>\n",
       "      <td>14.535653</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$b_0$</th>\n",
       "      <td>1.307798e-01</td>\n",
       "      <td>1.661310e-01</td>\n",
       "      <td>2.459237e-01</td>\n",
       "      <td>0.482121</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SSE</th>\n",
       "      <td>5.001645e+01</td>\n",
       "      <td>4.307040e+01</td>\n",
       "      <td>3.527985e+01</td>\n",
       "      <td>39.676413</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              Additive  Multiplicative  Additive Dam  Multiplica Dam\n",
       "$\\alpha$  4.546195e-01    3.659543e-01  6.194917e-09        0.000190\n",
       "$\\beta$   3.682627e-25    2.230501e-20  2.244538e-10        0.000190\n",
       "$\\phi$             NaN             NaN  9.429509e-01        0.912804\n",
       "$\\gamma$  5.244412e-01    3.232564e-14  2.917832e-07        0.000000\n",
       "$l_0$     1.421751e+01    1.454813e+01  1.415722e+01       14.535653\n",
       "$b_0$     1.307798e-01    1.661310e-01  2.459237e-01        0.482121\n",
       "SSE       5.001645e+01    4.307040e+01  3.527985e+01       39.676413"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fit1 = ExponentialSmoothing(aust, seasonal_periods=4, trend='add', seasonal='add').fit(use_boxcox=True)\n",
    "fit2 = ExponentialSmoothing(aust, seasonal_periods=4, trend='add', seasonal='mul').fit(use_boxcox=True)\n",
    "fit3 = ExponentialSmoothing(aust, seasonal_periods=4, trend='add', seasonal='add', damped=True).fit(use_boxcox=True)\n",
    "fit4 = ExponentialSmoothing(aust, seasonal_periods=4, trend='add', seasonal='mul', damped=True).fit(use_boxcox=True)\n",
    "results=pd.DataFrame(index=[r\"$\\alpha$\",r\"$\\beta$\",r\"$\\phi$\",r\"$\\gamma$\",r\"$l_0$\",\"$b_0$\",\"SSE\"])\n",
    "params = ['smoothing_level', 'smoothing_slope', 'damping_slope', 'smoothing_seasonal', 'initial_level', 'initial_slope']\n",
    "results[\"Additive\"]       = [fit1.params[p] for p in params] + [fit1.sse]\n",
    "results[\"Multiplicative\"] = [fit2.params[p] for p in params] + [fit2.sse]\n",
    "results[\"Additive Dam\"]   = [fit3.params[p] for p in params] + [fit3.sse]\n",
    "results[\"Multiplica Dam\"] = [fit4.params[p] for p in params] + [fit4.sse]\n",
    "\n",
    "ax = aust.plot(figsize=(10,6), marker='o', color='black', title=\"Forecasts from Holt-Winters' multiplicative method\" )\n",
    "ax.set_ylabel(\"International visitor night in Australia (millions)\")\n",
    "ax.set_xlabel(\"Year\")\n",
    "fit1.fittedvalues.plot(ax=ax, style='--', color='red')\n",
    "fit2.fittedvalues.plot(ax=ax, style='--', color='green')\n",
    "\n",
    "fit1.forecast(8).rename('Holt-Winters (add-add-seasonal)').plot(ax=ax, style='--', marker='o', color='red', legend=True)\n",
    "fit2.forecast(8).rename('Holt-Winters (add-mul-seasonal)').plot(ax=ax, style='--', marker='o', color='green', legend=True)\n",
    "\n",
    "plt.show()\n",
    "print(\"Figure 7.6: Forecasting international visitor nights in Australia using Holt-Winters method with both additive and multiplicative seasonality.\")\n",
    "\n",
    "results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Internals\n",
    "It is possible to get at the internals of the Exponential Smoothing models. \n",
    "\n",
    "Here we show some tables that allow you to view side by side the original values $y_t$, the level $l_t$, the trend $b_t$, the season $s_t$ and the fitted values $\\hat{y}_t$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-12-07T12:39:28.399765Z",
     "start_time": "2017-12-07T12:39:28.377215Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>$\\hat{y}_t$</th>\n",
       "      <th>$b_t$</th>\n",
       "      <th>$l_t$</th>\n",
       "      <th>$s_t$</th>\n",
       "      <th>$y_t$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2005-01-01</th>\n",
       "      <td>41.721187</td>\n",
       "      <td>-34.969347</td>\n",
       "      <td>49.317633</td>\n",
       "      <td>-7.593361</td>\n",
       "      <td>41.7275</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2005-04-01</th>\n",
       "      <td>24.190140</td>\n",
       "      <td>-35.452863</td>\n",
       "      <td>49.932500</td>\n",
       "      <td>-25.834764</td>\n",
       "      <td>24.0418</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2005-07-01</th>\n",
       "      <td>31.460571</td>\n",
       "      <td>-36.532814</td>\n",
       "      <td>51.126191</td>\n",
       "      <td>-19.182983</td>\n",
       "      <td>32.3281</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2005-10-01</th>\n",
       "      <td>36.634794</td>\n",
       "      <td>-37.397653</td>\n",
       "      <td>52.210127</td>\n",
       "      <td>-15.209719</td>\n",
       "      <td>37.3287</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-01-01</th>\n",
       "      <td>45.097746</td>\n",
       "      <td>-38.467239</td>\n",
       "      <td>53.476756</td>\n",
       "      <td>-7.837219</td>\n",
       "      <td>46.2132</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-04-01</th>\n",
       "      <td>27.191719</td>\n",
       "      <td>-40.276306</td>\n",
       "      <td>55.513851</td>\n",
       "      <td>-27.017395</td>\n",
       "      <td>29.3463</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-07-01</th>\n",
       "      <td>36.544237</td>\n",
       "      <td>-40.625044</td>\n",
       "      <td>56.224484</td>\n",
       "      <td>-19.713855</td>\n",
       "      <td>36.4829</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-10-01</th>\n",
       "      <td>41.449495</td>\n",
       "      <td>-42.041755</td>\n",
       "      <td>57.766085</td>\n",
       "      <td>-15.523317</td>\n",
       "      <td>42.9777</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2007-01-01</th>\n",
       "      <td>50.934536</td>\n",
       "      <td>-41.543801</td>\n",
       "      <td>57.536738</td>\n",
       "      <td>-7.588644</td>\n",
       "      <td>48.9015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2007-04-01</th>\n",
       "      <td>31.418282</td>\n",
       "      <td>-42.197826</td>\n",
       "      <td>58.150998</td>\n",
       "      <td>-26.874255</td>\n",
       "      <td>31.1802</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2007-07-01</th>\n",
       "      <td>38.718323</td>\n",
       "      <td>-42.303497</td>\n",
       "      <td>58.363015</td>\n",
       "      <td>-20.191939</td>\n",
       "      <td>37.7179</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2007-10-01</th>\n",
       "      <td>44.140694</td>\n",
       "      <td>-41.085795</td>\n",
       "      <td>57.181905</td>\n",
       "      <td>-14.982776</td>\n",
       "      <td>40.4202</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008-01-01</th>\n",
       "      <td>49.315775</td>\n",
       "      <td>-42.961522</td>\n",
       "      <td>58.853040</td>\n",
       "      <td>-8.619919</td>\n",
       "      <td>51.2069</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008-04-01</th>\n",
       "      <td>32.307045</td>\n",
       "      <td>-43.186562</td>\n",
       "      <td>59.367029</td>\n",
       "      <td>-27.309192</td>\n",
       "      <td>31.8872</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008-07-01</th>\n",
       "      <td>39.207459</td>\n",
       "      <td>-44.827029</td>\n",
       "      <td>61.095651</td>\n",
       "      <td>-20.925629</td>\n",
       "      <td>40.9783</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008-10-01</th>\n",
       "      <td>44.551221</td>\n",
       "      <td>-44.899546</td>\n",
       "      <td>61.462258</td>\n",
       "      <td>-17.320017</td>\n",
       "      <td>43.7725</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-01-01</th>\n",
       "      <td>54.358196</td>\n",
       "      <td>-46.192262</td>\n",
       "      <td>62.816880</td>\n",
       "      <td>-7.881650</td>\n",
       "      <td>55.5586</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-04-01</th>\n",
       "      <td>35.153874</td>\n",
       "      <td>-45.980223</td>\n",
       "      <td>62.832214</td>\n",
       "      <td>-28.447929</td>\n",
       "      <td>33.8509</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-07-01</th>\n",
       "      <td>43.066557</td>\n",
       "      <td>-46.228144</td>\n",
       "      <td>63.082697</td>\n",
       "      <td>-20.550663</td>\n",
       "      <td>42.0764</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-10-01</th>\n",
       "      <td>45.871140</td>\n",
       "      <td>-46.852574</td>\n",
       "      <td>63.748933</td>\n",
       "      <td>-17.997909</td>\n",
       "      <td>45.6423</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-01-01</th>\n",
       "      <td>57.166692</td>\n",
       "      <td>-48.770431</td>\n",
       "      <td>65.777639</td>\n",
       "      <td>-7.372159</td>\n",
       "      <td>59.7668</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-04-01</th>\n",
       "      <td>36.761367</td>\n",
       "      <td>-48.308398</td>\n",
       "      <td>65.650096</td>\n",
       "      <td>-29.816920</td>\n",
       "      <td>35.1919</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-07-01</th>\n",
       "      <td>44.932527</td>\n",
       "      <td>-48.798715</td>\n",
       "      <td>66.119516</td>\n",
       "      <td>-21.517549</td>\n",
       "      <td>44.3197</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-10-01</th>\n",
       "      <td>48.399593</td>\n",
       "      <td>-49.269882</td>\n",
       "      <td>66.667506</td>\n",
       "      <td>-18.522361</td>\n",
       "      <td>47.9137</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2011-01-01</th>\n",
       "      <td>61.338091</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2011-04-01</th>\n",
       "      <td>37.242885</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2011-07-01</th>\n",
       "      <td>46.842697</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2011-10-01</th>\n",
       "      <td>51.005342</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-01</th>\n",
       "      <td>64.471043</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-04-01</th>\n",
       "      <td>39.777012</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-07-01</th>\n",
       "      <td>49.636014</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-10-01</th>\n",
       "      <td>53.901644</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            $\\hat{y}_t$      $b_t$      $l_t$      $s_t$    $y_t$\n",
       "2005-01-01    41.721187 -34.969347  49.317633  -7.593361  41.7275\n",
       "2005-04-01    24.190140 -35.452863  49.932500 -25.834764  24.0418\n",
       "2005-07-01    31.460571 -36.532814  51.126191 -19.182983  32.3281\n",
       "2005-10-01    36.634794 -37.397653  52.210127 -15.209719  37.3287\n",
       "2006-01-01    45.097746 -38.467239  53.476756  -7.837219  46.2132\n",
       "2006-04-01    27.191719 -40.276306  55.513851 -27.017395  29.3463\n",
       "2006-07-01    36.544237 -40.625044  56.224484 -19.713855  36.4829\n",
       "2006-10-01    41.449495 -42.041755  57.766085 -15.523317  42.9777\n",
       "2007-01-01    50.934536 -41.543801  57.536738  -7.588644  48.9015\n",
       "2007-04-01    31.418282 -42.197826  58.150998 -26.874255  31.1802\n",
       "2007-07-01    38.718323 -42.303497  58.363015 -20.191939  37.7179\n",
       "2007-10-01    44.140694 -41.085795  57.181905 -14.982776  40.4202\n",
       "2008-01-01    49.315775 -42.961522  58.853040  -8.619919  51.2069\n",
       "2008-04-01    32.307045 -43.186562  59.367029 -27.309192  31.8872\n",
       "2008-07-01    39.207459 -44.827029  61.095651 -20.925629  40.9783\n",
       "2008-10-01    44.551221 -44.899546  61.462258 -17.320017  43.7725\n",
       "2009-01-01    54.358196 -46.192262  62.816880  -7.881650  55.5586\n",
       "2009-04-01    35.153874 -45.980223  62.832214 -28.447929  33.8509\n",
       "2009-07-01    43.066557 -46.228144  63.082697 -20.550663  42.0764\n",
       "2009-10-01    45.871140 -46.852574  63.748933 -17.997909  45.6423\n",
       "2010-01-01    57.166692 -48.770431  65.777639  -7.372159  59.7668\n",
       "2010-04-01    36.761367 -48.308398  65.650096 -29.816920  35.1919\n",
       "2010-07-01    44.932527 -48.798715  66.119516 -21.517549  44.3197\n",
       "2010-10-01    48.399593 -49.269882  66.667506 -18.522361  47.9137\n",
       "2011-01-01    61.338091        NaN        NaN        NaN      NaN\n",
       "2011-04-01    37.242885        NaN        NaN        NaN      NaN\n",
       "2011-07-01    46.842697        NaN        NaN        NaN      NaN\n",
       "2011-10-01    51.005342        NaN        NaN        NaN      NaN\n",
       "2012-01-01    64.471043        NaN        NaN        NaN      NaN\n",
       "2012-04-01    39.777012        NaN        NaN        NaN      NaN\n",
       "2012-07-01    49.636014        NaN        NaN        NaN      NaN\n",
       "2012-10-01    53.901644        NaN        NaN        NaN      NaN"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame(np.c_[aust, fit1.level, fit1.slope, fit1.season, fit1.fittedvalues],\n",
    "                  columns=[r'$y_t$',r'$l_t$',r'$b_t$',r'$s_t$',r'$\\hat{y}_t$'],index=aust.index)\n",
    "df.append(fit1.forecast(8).rename(r'$\\hat{y}_t$').to_frame(), sort=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-12-07T12:39:28.574783Z",
     "start_time": "2017-12-07T12:39:28.401234Z"
    }
   },
   "outputs": [
    {
     "data": {
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       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>$\\hat{y}_t$</th>\n",
       "      <th>$b_t$</th>\n",
       "      <th>$l_t$</th>\n",
       "      <th>$s_t$</th>\n",
       "      <th>$y_t$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2005-01-01</th>\n",
       "      <td>41.860083</td>\n",
       "      <td>-36.530008</td>\n",
       "      <td>51.244264</td>\n",
       "      <td>0.815912</td>\n",
       "      <td>41.7275</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2005-04-01</th>\n",
       "      <td>25.838562</td>\n",
       "      <td>-35.866508</td>\n",
       "      <td>50.735884</td>\n",
       "      <td>0.495386</td>\n",
       "      <td>24.0418</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2005-07-01</th>\n",
       "      <td>31.659199</td>\n",
       "      <td>-37.283697</td>\n",
       "      <td>52.060128</td>\n",
       "      <td>0.613003</td>\n",
       "      <td>32.3281</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2005-10-01</th>\n",
       "      <td>35.189590</td>\n",
       "      <td>-39.169019</td>\n",
       "      <td>54.186726</td>\n",
       "      <td>0.664199</td>\n",
       "      <td>37.3287</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-01-01</th>\n",
       "      <td>44.929236</td>\n",
       "      <td>-40.305867</td>\n",
       "      <td>55.705557</td>\n",
       "      <td>0.815071</td>\n",
       "      <td>46.2132</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-04-01</th>\n",
       "      <td>27.933758</td>\n",
       "      <td>-42.087347</td>\n",
       "      <td>57.755897</td>\n",
       "      <td>0.493067</td>\n",
       "      <td>29.3463</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-07-01</th>\n",
       "      <td>35.824552</td>\n",
       "      <td>-43.100241</td>\n",
       "      <td>59.126764</td>\n",
       "      <td>0.610109</td>\n",
       "      <td>36.4829</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-10-01</th>\n",
       "      <td>39.768810</td>\n",
       "      <td>-45.643918</td>\n",
       "      <td>61.906725</td>\n",
       "      <td>0.661722</td>\n",
       "      <td>42.9777</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2007-01-01</th>\n",
       "      <td>51.174860</td>\n",
       "      <td>-45.121007</td>\n",
       "      <td>61.855817</td>\n",
       "      <td>0.813613</td>\n",
       "      <td>48.9015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2007-04-01</th>\n",
       "      <td>30.814592</td>\n",
       "      <td>-46.408345</td>\n",
       "      <td>63.134595</td>\n",
       "      <td>0.490311</td>\n",
       "      <td>31.1802</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2007-07-01</th>\n",
       "      <td>39.009304</td>\n",
       "      <td>-46.386327</td>\n",
       "      <td>63.326690</td>\n",
       "      <td>0.608241</td>\n",
       "      <td>37.7179</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2007-10-01</th>\n",
       "      <td>42.486058</td>\n",
       "      <td>-46.170605</td>\n",
       "      <td>63.142969</td>\n",
       "      <td>0.660460</td>\n",
       "      <td>40.4202</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008-01-01</th>\n",
       "      <td>52.174279</td>\n",
       "      <td>-46.759202</td>\n",
       "      <td>63.700961</td>\n",
       "      <td>0.813405</td>\n",
       "      <td>51.2069</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008-04-01</th>\n",
       "      <td>31.677344</td>\n",
       "      <td>-47.835482</td>\n",
       "      <td>64.870076</td>\n",
       "      <td>0.489567</td>\n",
       "      <td>31.8872</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008-07-01</th>\n",
       "      <td>40.035793</td>\n",
       "      <td>-49.239196</td>\n",
       "      <td>66.467167</td>\n",
       "      <td>0.607691</td>\n",
       "      <td>40.9783</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008-10-01</th>\n",
       "      <td>44.516009</td>\n",
       "      <td>-49.574968</td>\n",
       "      <td>67.064687</td>\n",
       "      <td>0.659599</td>\n",
       "      <td>43.7725</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-01-01</th>\n",
       "      <td>55.343530</td>\n",
       "      <td>-50.602062</td>\n",
       "      <td>68.189009</td>\n",
       "      <td>0.812788</td>\n",
       "      <td>55.5586</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-04-01</th>\n",
       "      <td>33.773212</td>\n",
       "      <td>-51.515117</td>\n",
       "      <td>69.284003</td>\n",
       "      <td>0.487892</td>\n",
       "      <td>33.8509</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-07-01</th>\n",
       "      <td>42.644318</td>\n",
       "      <td>-52.025168</td>\n",
       "      <td>69.970005</td>\n",
       "      <td>0.606391</td>\n",
       "      <td>42.0764</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-10-01</th>\n",
       "      <td>46.778466</td>\n",
       "      <td>-52.310493</td>\n",
       "      <td>70.364950</td>\n",
       "      <td>0.658710</td>\n",
       "      <td>45.6423</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-01-01</th>\n",
       "      <td>58.009255</td>\n",
       "      <td>-54.093644</td>\n",
       "      <td>72.211000</td>\n",
       "      <td>0.812310</td>\n",
       "      <td>59.7668</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-04-01</th>\n",
       "      <td>35.648489</td>\n",
       "      <td>-54.499636</td>\n",
       "      <td>72.908994</td>\n",
       "      <td>0.486533</td>\n",
       "      <td>35.1919</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-07-01</th>\n",
       "      <td>44.784417</td>\n",
       "      <td>-55.163557</td>\n",
       "      <td>73.682480</td>\n",
       "      <td>0.605417</td>\n",
       "      <td>44.3197</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-10-01</th>\n",
       "      <td>49.174497</td>\n",
       "      <td>-55.389255</td>\n",
       "      <td>74.029064</td>\n",
       "      <td>0.657842</td>\n",
       "      <td>47.9137</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2011-01-01</th>\n",
       "      <td>60.967584</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2011-04-01</th>\n",
       "      <td>36.993906</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2011-07-01</th>\n",
       "      <td>46.712499</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2011-10-01</th>\n",
       "      <td>51.482851</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-01</th>\n",
       "      <td>64.456575</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-04-01</th>\n",
       "      <td>39.017379</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-07-01</th>\n",
       "      <td>49.291936</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-10-01</th>\n",
       "      <td>54.320270</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            $\\hat{y}_t$      $b_t$      $l_t$     $s_t$    $y_t$\n",
       "2005-01-01    41.860083 -36.530008  51.244264  0.815912  41.7275\n",
       "2005-04-01    25.838562 -35.866508  50.735884  0.495386  24.0418\n",
       "2005-07-01    31.659199 -37.283697  52.060128  0.613003  32.3281\n",
       "2005-10-01    35.189590 -39.169019  54.186726  0.664199  37.3287\n",
       "2006-01-01    44.929236 -40.305867  55.705557  0.815071  46.2132\n",
       "2006-04-01    27.933758 -42.087347  57.755897  0.493067  29.3463\n",
       "2006-07-01    35.824552 -43.100241  59.126764  0.610109  36.4829\n",
       "2006-10-01    39.768810 -45.643918  61.906725  0.661722  42.9777\n",
       "2007-01-01    51.174860 -45.121007  61.855817  0.813613  48.9015\n",
       "2007-04-01    30.814592 -46.408345  63.134595  0.490311  31.1802\n",
       "2007-07-01    39.009304 -46.386327  63.326690  0.608241  37.7179\n",
       "2007-10-01    42.486058 -46.170605  63.142969  0.660460  40.4202\n",
       "2008-01-01    52.174279 -46.759202  63.700961  0.813405  51.2069\n",
       "2008-04-01    31.677344 -47.835482  64.870076  0.489567  31.8872\n",
       "2008-07-01    40.035793 -49.239196  66.467167  0.607691  40.9783\n",
       "2008-10-01    44.516009 -49.574968  67.064687  0.659599  43.7725\n",
       "2009-01-01    55.343530 -50.602062  68.189009  0.812788  55.5586\n",
       "2009-04-01    33.773212 -51.515117  69.284003  0.487892  33.8509\n",
       "2009-07-01    42.644318 -52.025168  69.970005  0.606391  42.0764\n",
       "2009-10-01    46.778466 -52.310493  70.364950  0.658710  45.6423\n",
       "2010-01-01    58.009255 -54.093644  72.211000  0.812310  59.7668\n",
       "2010-04-01    35.648489 -54.499636  72.908994  0.486533  35.1919\n",
       "2010-07-01    44.784417 -55.163557  73.682480  0.605417  44.3197\n",
       "2010-10-01    49.174497 -55.389255  74.029064  0.657842  47.9137\n",
       "2011-01-01    60.967584        NaN        NaN       NaN      NaN\n",
       "2011-04-01    36.993906        NaN        NaN       NaN      NaN\n",
       "2011-07-01    46.712499        NaN        NaN       NaN      NaN\n",
       "2011-10-01    51.482851        NaN        NaN       NaN      NaN\n",
       "2012-01-01    64.456575        NaN        NaN       NaN      NaN\n",
       "2012-04-01    39.017379        NaN        NaN       NaN      NaN\n",
       "2012-07-01    49.291936        NaN        NaN       NaN      NaN\n",
       "2012-10-01    54.320270        NaN        NaN       NaN      NaN"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame(np.c_[aust, fit2.level, fit2.slope, fit2.season, fit2.fittedvalues], \n",
    "                  columns=[r'$y_t$',r'$l_t$',r'$b_t$',r'$s_t$',r'$\\hat{y}_t$'],index=aust.index)\n",
    "df.append(fit2.forecast(8).rename(r'$\\hat{y}_t$').to_frame(), sort=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally lets look at the levels, slopes/trends and seasonal components of the models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-12-07T12:39:29.636548Z",
     "start_time": "2017-12-07T12:39:28.576279Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "states1 = pd.DataFrame(np.c_[fit1.level, fit1.slope, fit1.season], columns=['level','slope','seasonal'], index=aust.index)\n",
    "states2 = pd.DataFrame(np.c_[fit2.level, fit2.slope, fit2.season], columns=['level','slope','seasonal'], index=aust.index)\n",
    "fig, [[ax1, ax4],[ax2, ax5], [ax3, ax6]] = plt.subplots(3, 2, figsize=(12,8))\n",
    "states1[['level']].plot(ax=ax1)\n",
    "states1[['slope']].plot(ax=ax2)\n",
    "states1[['seasonal']].plot(ax=ax3)\n",
    "states2[['level']].plot(ax=ax4)\n",
    "states2[['slope']].plot(ax=ax5)\n",
    "states2[['seasonal']].plot(ax=ax6)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "hide_input": false,
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.1"
  },
  "latex_envs": {
   "LaTeX_envs_menu_present": true,
   "autocomplete": true,
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
    "itemize": "Ctrl-I"
   },
   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
  },
  "toc": {
   "colors": {
    "hover_highlight": "#DAA520",
    "navigate_num": "#000000",
    "navigate_text": "#333333",
    "running_highlight": "#FF0000",
    "selected_highlight": "#FFD700",
    "sidebar_border": "#EEEEEE",
    "wrapper_background": "#FFFFFF"
   },
   "moveMenuLeft": true,
   "nav_menu": {
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 },
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}
